This invention relates generally to aircraft landing gear braking systems, and more particularly concerns an improved system for controlling aircraft brake pressure.
A conventional skid detection system used in aircraft braking systems typically includes a wheel speed transducer for each wheel brake of the wheels of the aircraft, for measuring wheel speed and generating wheel speed signals that are a function of the rotational speed of the brake wheel. The wheel speed signal is typically converted to a signal representing the velocity of the aircraft, and compared with a desired reference velocity, to generate wheel velocity error signals indicative of the difference between the wheel velocity signals from each braked wheel and the reference velocity signal. The output of the velocity comparator is referred to as velocity error. The velocity error signals typically are adjusted by a pressure bias modulator (PBM) integrator, a proportional control unit, and a compensation network, the outputs of which are summed to provide an anti-skid control signal received by the command processor. The PBM integrator in the antiskid loop dictates the maximum allowable control pressure level during braking. When no skid is detected, this integrator allows full system pressure to the brakes.
The conventional PID controller for aircraft brake control systems deals with various conditions such as aerodynamics, landing gear dynamics, xcexc-slip profile, different landing conditions, and the like. One major problem is that tuning of controller parameters to guarantee high efficiency in different landing conditions and conditions affecting the tire-runway coefficient of friction (xcexc) of the aircraft braking system is often a difficult task.
Such algorithms usually take only one input, i.e., wheel velocity (Vw), and determine a reference velocity (Vref) with an apparatus. Then the Vref and Vw signals pass through the PID control logic, which generates a command signal. The command signal is supplied to a hydraulic servo valve and the output of servo valve, fluid pressure generates a brake torque through a brake. The algorithms show good antiskid performancexe2x80x94robustness and adaptability.
In spite of success of the PID type controller, related industry engineers and researchers have been continuously investigating other control schemes, partially because of difficulty in antiskid braking control parameter tuning. A need therefore still exists for an antiskid braking controller that can facilitate and shorten the process of antiskid braking control parameter tuning. The present invention meets these and other needs.
Briefly, and in general terms, the present invention provides for a sliding integral proportional (SIP) controller for aircraft antiskid braking control that improves and shortens the time required for antiskid braking control parameter tuning, and that also provides higher braking efficiency, robustness, and adaptability, since the antiskid braking control parameters to be tuned are adjusted based on an accurate adaptive threshold and an velocity error ratio or modified slip ratio (Smod) signal with an estimated net wheel torque, a few integral gains, and a proportional gain. The proposed SIP controller requires only one input, and shows excellent braking efficiencies, robustness, and adaptability with only a fraction of tuning effort and time.
The present invention accordingly provides for a sliding, integral, and proportional (SIP) controller for providing anti-skid braking control for an aircraft. The SIP controller includes a reference velocity subsystem generating a reference velocity signal based upon an input wheel velocity signal; a velocity error ratio subsystem generating a modified slip ratio signal (Smod) based upon a ratio of the difference between the reference velocity and the wheel velocity to the reference velocity; and a main controller subsystem receiving the reference velocity signal and the modified slip ratio signal, and generating a control command output signal indicative of a command braking pressure.
In one embodiment, the reference velocity subsystem receives a plurality of sampled wheel velocity signals, determines a minimum value of the sampled wheel velocity signals, and compares the minimum value with an individual wheel velocity signal. If the minimum value of the sampled wheel velocity signals is greater than the wheel velocity signal, a predetermined desired reduction amount is subtracted from the minimum value of the sampled wheel velocity signals and the result is output as the reference velocity of the reference velocity subsystem. Otherwise the wheel velocity signal is output as the reference velocity of the reference velocity subsystem. In one aspect, the sampled wheel velocity signals have a predetermined fixed sampling time. In a present embodiment, the modified slip ratio signal (Smod) is determined based upon the equation:       S    mod    =      Velerror    Vref  
where Smod is the velocity error ratio or modified slip ratio, Vref is the reference velocity in radians per second, and Velerror is the velocity error in radians per second, determined from the equation Vrefxe2x88x92Vw, where Vw is the wheel velocity in radians per second.
In a present embodiment, the main controller subsystem includes a one dimensional sliding mode controller subsystem to determine an estimated net wheel torque signal; an adaptive threshold subsystem for generating an adaptive threshold based upon the modified slip ratio signal (Smod) and a clock signal; a first integral gain subsystem for comparing the estimated net wheel torque signal with the adaptive threshold to determine dominance between the tire drag torque and braking torque, and outputting a corresponding gain value; a second integral gain subsystem exponentially generating a deep skid signal (deep_skid) when the Smod signal is greater than a predetermined limit and a change in wheel velocity indicates a deep skid situation; a third integral gain subsystem to avoid Smod signals that are too small or negative and to modify the initial braking command signal; a proportional controller subsystem generating an output signal to prevent sudden deep skids; and a pressure limiter for limiting the command braking pressure. In one aspect of the invention, the output of the main controller subsystem is a command signal indicative of a torque, which is converted to a command brake pressure signal by multiplication of a predetermined gain.
The estimated net wheel torque may be determined based upon the velocity estimation error. One-dimensional sliding surface condition takes a form as:                                           1            2                    ⁢                      ⅆ                          ⅆ              t                                ⁢                      s            2                          =                              s            ⁢                                          ∂                Vref                                            ∂                t                                              -                                    Gain2                              Im                ⁢                                  xe2x80x83                                ⁢                w                                      ⁢                          "LeftBracketingBar"              s              "RightBracketingBar"                                                          (        1        )            
where s=Vrefxe2x88x92{circumflex over (V)}, Vref is the reference velocity in radians per second, {circumflex over (V)} is the observed or estimated wheel velocity in radians per second, Gain2 is determined as the largest possible net wheel torque in ft-lbs, and Imw is the wheel/tire/brake mass moment of inertia in slug-ft2. The equation (1) is always less than zero, and thus, the sliding condition is satisfied. The net wheel torque signal may be determined according to the equation:                                           ∂                          V              ^                                            ∂            t                          =                              Gain2                          Im              ⁢                              xe2x80x83                            ⁢              w                                ⁢                      sgn            ⁡                          (              s              )                                                          (        2        )            
where sg n(s) is the sign of s. The net wheel torque signal optionally may be determined according to the equation:
NWTe=DFxc3x97sgn(s)xc3x97Gain2xe2x80x83xe2x80x83(3)
where NWTe is the estimated net wheel torque in ft-lbs, and DF is a discrete filter of time constant, 0.1 sec. The low pass filter DF may be defined according to the equation:   DF  =      0.04877          z      -      0.9512      
where z is a complex variable.
In one embodiment of the invention, a plurality of skid levels are established to effectively maintain a tire drag friction coefficient (xcexc) approaching the peak value of xcexc without undesirable deep skid. In one present aspect, three skid levels are established. Thus, for example, if the Smod signal exceeds a first skid level threshold, the adaptive threshold increases to a second skid level threshold to accommodate a braking torque and prevent a slip overshoot by a predetermined rate; if the Smod signal is reduced below the second skid level threshold, the threshold decreases to supply an appropriate braking command and maintain the slip at the peak of xcexc; and the adaptive threshold becomes a third skid level threshold greater than the second skid level threshold and the Smod signal when the runway condition is very dry and tire drag coefficient is more than a predetermined threshold drag coefficient value, to generate a rapid initial braking command signal. In one present aspect, if the tire drag coefficient value is high (more than 0.5), then the rapid initial braking command signal is generated for approximately 0-1.5 seconds period after braking is initiated.
In a present embodiment, the first integral gain subsystem outputs a first positive gain value as the integral gain output if the estimated net wheel torque is greater than or equal to the adaptive threshold, indicating that the tire drag torque is dominant, and outputs a second negative gain value as the integral gain output if the estimated net wheel torque is less than the adaptive threshold.
In another present aspect of the invention, if Smod is greater than the deep skid limitation (Slim) of the Smod signal, and if the wheel velocity (Vw) is less than an immediately previous wheel velocity, then the deep skid signal (deep_skid) is determined according to the following equation:
deep_skid=Ta3*exp(u)xe2x80x83xe2x80x83(4)
where Ta3 is the first coefficient, and is a changing negative variable determined in a look-up table based upon the reference velocity, and u is the Smod skid level determined by the following equation:   u  =            (                        S          mod                -                  S          lim                    )        0.01  
In another aspect, the variable Ta3 changes to approximately zero at a predetermined reference velocity, causing an increase in the brake pressure and wheel lock-up. If the wheel velocity (Vw) is greater than or equal to an immediately previous wheel velocity when Smod is greater than or equal to Slim, then a second positive coefficient Ta3a is substituted for Ta3. In another aspect, if Smod is less than a constant value (Sneg), and if the elapsed time from the initiation of braking is less than about 1 second, then the output of the third integral gain subsystem is a predetermined constant, multiplied by a predetermined gain. In another present aspect, if Smod is less than a predetermined maximum threshold, the output signal of the proportional controller subsystem is zero.
In another present embodiment, if the product of the reference velocity (Vref) and the tire rolling radius is less than a predetermined threshold (Pdropout), the output signal of the proportional controller subsystem is a predetermined constant. If the product of the reference velocity (Vref) and the tire rolling radius is greater than or equal to the predetermined threshold (Pdropout), then the output signal of the proportional controller subsystem is the product of the velocity error and a predetermined negative gain. In another present aspect of the invention, the pressure limiter limits the command braking pressure between about 0 and about 3000 psi.
In another present embodiment, the invention further comprises a look-up table for converting the control command output signal indicative of the command braking pressure to a control command indicative of the command control current. In a present aspect, the look-up table describes a nonlinear pressure vs. current relationship. In another present embodiment, the invention further comprises a current limiter for limiting the command control current up to about 60 mA.
The present invention also provides a method for providing sliding, integral, and proportional anti-skid braking control for an aircraft having a plurality of tires and brakes. An input wheel velocity signal is provided, and a reference velocity signal is generated based upon the input wheel velocity signal. A modified slip ratio signal (Smod) is then generated based upon a ratio of the difference between the reference velocity and the wheel velocity to the reference velocity, and a control command output signal indicative of a command braking pressure is generated based upon the reference velocity signal and the modified slip ratio signal. In a present aspect of the method, a plurality of sampled wheel velocity signals are provided, and a minimum value of the sampled wheel velocity signals is determined. The minimum value is compared with individual wheel velocity signals, and if the minimum value of the sampled wheel velocity signals is greater than an individual wheel velocity signal, a predetermined desired reduction amount is subtracted from the minimum value of the sampled wheel velocity signals and the result is output as the reference velocity. Otherwise the wheel velocity signal is output as the reference velocity. In a present aspect of the method, the sampled wheel velocity signals have a predetermined fixed sampling time.
In another aspect of the method of the invention, an estimated net wheel torque signal is determined, an adaptive threshold is generated based upon the modified slip ratio signal (Smod) and a clock signal, the estimated net wheel torque signal is compared with the adaptive threshold to determine dominance between the tire drag torque and braking torque, and a corresponding first integral gain value is output. A deep skid signal (deep_skid) is exponentially generated when the Smod signal is greater than a predetermined deep slid limitation (Slim) and wheel velocities indicate a deep skid situation, based upon the modified slip ratio signal (Smod), the wheel velocity signal (Vw), the reference velocity signal (Vref), the tire rolling radius, a predetermined deep skid limitation (Slim) of the Smod signal, and first and second function coefficients. The initial braking command signal is modified to avoid Smod signals that are too small or negative; an output signal is generated to prevent sudden deep skids; and the command braking pressure is limited to a maximum amount.
The present invention also provides for a method for determining braking efficiency of an aircraft braking system independent of the specific conditions. A new xcexcefficiency (xcex7) is determined based upon an antiskid braking efficiency (xcexcb), average braking force (A) of all the non-braking forces acting to stop, or accelerate the aircraft, and the average braking force (B) of the aircraft braking system, according to the following equation:                     η        =                              A            +                                          μ                b                            ·              B                                            A            +            B                                              (        6        )            
where A is the force of all the non-braking forces acting to stop, or accelerate the aircraft; B is the force of the aircraft braking system, and xcexcb is the antiskid braking efficiency, determined as the actual tire drag coefficient xcexc divided by the peak tire drag coefficient xcexc.